Low Degree Fields Unramified Outside of {∞, 7, 13, 29}

Discriminant class: −2639

∞ 7 13 29 a_{1} a_{2} a_{3} Over p = 7  Over p = 13  Over p = 29 2 3 5 11 17 19 23 31
G h  f^{e} c_{w} d s f^{e} c_{w} d  s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
1. 1_{k} 1_{k} 1_{−} 1_{+} 0 2639  1^{2} 1_{k} 7 7 1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{+} 29 29  2  2
C_{2} 64  2 2 2  2

Discriminant class: −203

∞ 7 13 29 a_{1} a_{2} a_{3} Over p = 7 Over p = 13 Over p = 29 2 3 5 11 17 19 23 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
2. 1_{k} 1_{i} 0_{+} 1_{+} 0 203  1^{2} 1_{i} 7∗ 7∗ 2 0_{+} ∗ ∗ 1^{2} 1_{+} 29 29 2  2 2
C_{2} 4  2  2  2

Discriminant class: −91

∞ 7 13 29 a_{1} a_{2} a_{3} Over p = 7  Over p = 13  Over p = 29 2 3 5 11 17 19 23 31
G h  f^{e} c_{w} d s f^{e} c_{w} d  s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
3. 1_{k} 1_{k} 1_{−} 0_{+} 0 91  1^{2} 1_{k} 7 7 1^{2} 1_{−} 13∗ 13∗  2 2  2 2
C_{2} 2  2  2 2

Discriminant class: −7

∞ 7 13 29 a_{1} a_{2} a_{3} Over p = 7 Over p = 13 Over p = 29 2 3 5 11 17 19 23 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
4. 1_{k} 1_{i} 0_{+} 0_{+} 1 2  1^{2} 1_{i} 7∗ 7∗ 2 0_{+} ∗ ∗  2 2  2 2  2
C_{2}  2  2  2 2

Discriminant class: 1

∞ 7 13 29 a_{1} a_{2} a_{3} Over p = 7  Over p = 13 Over p = 29 2 3 5 11 17 19 23 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
5. 0_{+} 2_{+} 0_{+} 0_{+} -1 -2 1 1^{3} 2_{+} 1  3 3 3 3 3 3 3 3
C_{3}  3  3 3 3 3 3
6. 0_{+} 0_{+} 2_{+} 0_{+} -1 -4 -1 3 0_{+} 1  1^{3} 2_{+} 1  3 0_{+} 1  3 3  3 3 3 3
C_{3}  3 3 3  3 3 3
7. 0_{+} 2_{+} 2_{+} 0_{+} -1 -30 64 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 0_{+} 1  3 3 3  3  3
C_{3} 3  3 3 3 3  3 3
8. 0_{+} 2_{+} 2_{+} 0_{+} 1 -30 27 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 0_{+} 1  3  3  3  3 3
C_{3} 3  3 3 3 3 3 3

Discriminant class: 13

∞ 7 13 29 a_{1} a_{2} a_{3} Over p = 7  Over p = 13  Over p = 29 2 3 5 11 17 19 23 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
9. 0_{+} 0_{+} 1_{+} 0_{+} 1 -3  2 0_{+} ∗ ∗ 1^{2} 1_{+} 13 13  2  2 2  2  2
C_{2}  2 2  2  2  2

Discriminant class: 29

∞ 7 13 29 a_{1} a_{2} a_{3} Over p = 7  Over p = 13  Over p = 29 2 3 5 11 17 19 23 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
10. 0_{+} 0_{+} 0_{+} 1_{+} 0 -29  1^{2} 1_{+} 29 29 2 2  2 2 2  2
C_{2}  2 2 2 2  2
11. 0_{+} 2_{+} 2_{+} 1_{+} -1 -121 246 1^{3} 2_{+} 1  1^{3} 2_{+} 1  1^{2} 1_{+} 29 29 2 2  2 2 2 3 2
S_{3} 9  2 2 2 2 3 3 2 3

Discriminant class: 377

∞ 7 13 29 a_{1} a_{2} a_{3} Over p = 7  Over p = 13  Over p = 29 2 3 5 11 17 19 23 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
12. 0_{+} 0_{+} 1_{+} 1_{+} 0 -377  2 0_{+} ∗ ∗ 1^{2} 1_{+} 13 13 1^{2} 1_{+} 29 29  2 2  2
C_{2} 2  2  2 2 2